If nothing happens, download Xcode and try again. Coursera Assignments. Â© 2020 Coursera Inc. All rights reserved. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in Python (functions, loops, recursion), common sense and curiosity. This means that actually, we can think it has no start and no end. Work fast with our official CLI. Video created by National Research University Higher School of Economics for the course "Discrete Math and Analyzing Social Graphs". The letters must look like similar to Latin letters, and Cyrillic letters like those that are depicted on the slides are not allowed. The Euler path is a specific path which visits each edge exactly once. Probability is everywhere in Data Analysis and we will study it in much more details later. Can you tell how many blue circles do you have in this picture without just counting them by hand? To view this video please enable JavaScript, and consider upgrading to a web browser that So a Euler path is a path in the graph. It has this Euler property, that each edge should be visited exactly once. Bridges are represented by edges, there are seven edges. So A could not be a vertex which is visited in the middle of our tour, but next, we see that all other vertices are the same, they're also odd, and thus Euler's problem is unsolvable. We will start with a brief introduction to combinatorics, the branch of mathematics that studies how to count. they're used to log you in. Basics of this topic are critical for anyone working in Data Analysis or Computer Science. We will use counting a lot to count probabilities, and we will need counting to estimate the size of data. We will illustrate new knowledge, for example, by counting the number of features in data or by estimating the time required for a Python program to run. they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. Let's count, how many edges come to A? The quiz and programming homework is belong to coursera and edx and solutions to me. Okay, counting is important, but still why do we study it? Isn't it a trivial task? supports HTML5 video. And the model gives us a prediction, will the customer like our product? Thanks to all the professors, teachers, staffs and coordinators for making this course so interesting. This repository is aimed to help Coursera learners who have difficulties in their learning process. Well, we want to walk along the city and visit each bridge exactly once. So there is a specific kind of Euler path which is called the Euler cycle. So the question is whether it is possible. To answer this question, we are going to represent our map as a graph, and you can see it on this picture. So at each visit, we'll use two bridges. We have 12 options for each letter, and the reason for this is the following. Suppose a country, a state, or religion introduces a new format of a license plate, and here is a Russian example. Find Test Answers Search for test and quiz questions and answers. This is proved exactly as we did in our example of the Konigsberg bridges. Well, if they coincide, then there should be one vertex and it should be even. To view this video please enable JavaScript, and consider upgrading to a web browser that, Acyclic Directed Graphs. Basics of this topic are critical for anyone working in Data Analysis or Computer Science. So it is important to estimate the number of all possible different objects just to tell how many data you will need to teach your model. We can take an arbitrary vertex on the Euler cycle, and we start from this vertex and we return to the same vertex. Graphs represent objects and relations between them in a compact geometric form. Very informative and practical. [Coursera] Introduction to Discrete Mathematics for Computer Science Specialization Topics coursera discrete-mathematics graph-theory combinatorics probability number-theory cryptography coursera-discrete-mathematics For example, for us the following applications will be important. The main goal of this course is to introduce topics in Discrete Mathematics relevant to Data Analysis. We have 10 options for each digit. Suppose that our tour starts at B and end at C. Now, A is a vertex which was visited in the middle. [MUSIC] Hi, I'm Vladimir Podolskii, and today we are going to study combinatorics, the field of mathematics that deals with counting. Topological Sorting. Repository for Coursera class Algorithm I & II by Princeton University. Learn more. We will start with a brief introduction to combinatorics, the branch of mathematics that studies how to count. For more information, see our Privacy Statement. Especially enjoyed learning the theory and Python practical in chunks and then bringing them together for the final assignment. Do we need to create a list of all our data entries to check whether we have enough data to teach our ML model? If nothing happens, download the GitHub extension for Visual Studio and try again. Therefore, if there exists a Euler cycle, then the graph has no odd vertices. Applications of graphs include geoinformational systems (vertices are cities, edges are roads), social network analysis (people and friendship relations), chemistry (graphs of molecular structure), computer network topology, and many more. Next, we will apply our knowledge in combinatorics to study basic Probability Theory. Here is another real life example we will discuss later in this course. The course has helped me grasp some important topics. Let us elaborate on this last example. And 78 on the right is a regional code. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in Python (functions, loops, recursion), common sense and curiosity. You can always update your selection by clicking Cookie Preferences at the bottom of the page. We will mainly concentrate in this course on the graphs of social networks. Millions of developers and companies build, ship, and maintain their software on GitHub — the largest and most advanced development platform in the world. It turns out that counting is used a lot in our parts of mathematics and applications. And how much data you need to teach a model? It is a Euler path which starts and ends at the same vertex. This repository is aimed to help Coursera and edX learners who have difficulties in their learning process. Thank you. The course has helped me grasp some important topics. Discrete Math and Analyzing Social Graphs, National Research University Higher School of Economics, Mathematics for Data Science Specialization, Construction Engineering and Management Certificate, Machine Learning for Analytics Certificate, Innovation Management & Entrepreneurship Certificate, Sustainabaility and Development Certificate, Spatial Data Analysis and Visualization Certificate, Master's of Innovation & Entrepreneurship. So it turns out that it is not always a trivial task, and there are many important ideas on how to count. Use Git or checkout with SVN using the web URL. Well, a path through the graph is a sequence of vertices which are connected by edges. Next, we will apply our knowledge in combinatorics to study basic Probability Theory. We have two islands that are denoted by A and D here, and we have two banks of the river C and B, and they are connected by seven bridges which can be seen on the map. We will start with a brief introduction to combinatorics, the branch of mathematics that studies how to count. So the number of bridges which are adjacent to A should be 2k. The quiz and programming homework is belong to coursera.Please Do Not use them for any other purposes. Discrete Math and Analyzing Social Graphs, National Research University Higher School of Economics, Mathematics for Data Science Specialization, Construction Engineering and Management Certificate, Machine Learning for Analytics Certificate, Innovation Management & Entrepreneurship Certificate, Sustainabaility and Development Certificate, Spatial Data Analysis and Visualization Certificate, Master's of Innovation & Entrepreneurship. Our intended audience are all people that work or plan to work in Data Analysis, starting from motivated high school students. Very informative and practical. So we start with a vertex, then we move to another one using an edge, and we do it until we end our path. Is there a way to tell whether our algorithm will run in a reasonable time before implementing and actually running it? We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. Applications of graphs include geoinformational systems (vertices are cities, edges are roads), social network analysis (people and friendship relations), chemistry (graphs of molecular structure), computer network topology, and many more.